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Real-time systems, ranging from small portable devices or embedded systems to more complex general-purpose computers, are designed to satisfy various ofreal-time computation. It is the most important toguarantee all the requests will be satisfied correctly intime. Rate monotonic algorithm is the most well-known real-time scheduling algorithm in the periodic task model. It not only has high schedulability, but alsohas a tight utilization bound to easily check whetherthe task set is feasible. In rate monotonic algorithm,a task will be executed once in each period, but thestart time of execution might be different in each period.On the contrary, for tasks scheduled using pinwheelmodel, the execution schedule in each period will be always the same. Therefore, pinwheel scheduling model is very suitable for real-time systems which need high predictability. The pinwheel scheduling model transforms the task periods into harmonic numbers shorter thanor equal to the original periods and provides many advantageous scheduling features. However, not all tasks allow to do the transformation and some would like tobe executed according to their original periods. In thispaper, we discuss how to solve the problem and give anapplication in power-aware real-time scheduling, wherewe can see the pinwheel model is very important in current embedded system design with power-aware requirement.